We utilize advanced physical and mathematical methods to understand the biophysics of complex cellular processes. Phenomena under study include the stochastic biogenesis of coated vesicles involved in endocytosis and other intracellular transport processes, and the structural organization of multicellular biofilms arising from the attachment of prokaryotes to surfaces in nutrient-rich environments. These studies are of interest to persons studying basic cell biological processes, but they also are relevant to disease processes and normal and abnormal tissue development. Each requires the integration of several complicated processes, utilizing information obtained through reductionist studies but here focusing on behaviors emerging from both synergistic and competitive interactions. We have constructed a complex, multi-element model of receptor mediated endocytosis that encompasses cargo recognition, phosphoinositide metabolism, and clathrin coat formation and dissolution. The analysis demonstrates how the inter-related kinetic elements of these processes determine whether an endocytic vesicle will form. Not only does the model explain how vesicle biogenesis is triggered by, e.g., the binding of ligands to receptors at specific sites, but it also can rationalize the observed probabilistic quality of cell response in the presence of a stimulus. To gather data needed to refine the model, we have performed Atomic Force Microscopic investigations of clathrin triskelia, devising a scheme for examining fluctuations in triskelial shape while free in solution. We also perfected a technique for viewing dry samples that yields triskelial morphology with resolution at least as good as that obtainable by electron microscopy (EM). The latter was used to examine the formation of assembly intermediates when the triskelia are allowed to polymerize into clathrin cages in low pH buffers. Another area of complex systems biology currently under investigation in our laboratory pertains to bacterial biofilms. The latter are surface-attached communities of microorganisms that express a polymer coating--the extracellular polymeric substance (EPS)--that protects the attached bacterial colonies from antimicrobial agents. Biofilms are ubiquitous in the natural and technologically-modified worlds, yet little is really understood about their formation and viability;in human disease many bacterial pathogens form biofilms which resist destruction, causing great distress for patients who are unfortunate enough to be infected. We have focused on measuring the mechanical and transport properties of the EPS as a function of environmental parameters such as pH and externally-induced shear forces. One goal of this research is to identify factors that affect the flow of antibiotics within a biofilm and to understand how the EPS mediatesthe activity of immune cells. Another is to understand how the transport of nutrients and signaling molecules within a film is coupled to the spatially-heterogenous structures that develop, with a view towards understanding how various agents might mediate the growth of the bacteria. We also are investigating how biofilms, which are amenable to external manipulation, can serve as rudimentary models for studying the growth and regeneration of more complex cell communities. In order to characterize the mechanical properties of the EPS, we have developed methods involving atomic force microscopy that allow us to take into account the spatial heterogeneity of the colonies. We have found that the soft, hydrated EPS gel, which consists mainly of polysaccharides, proteins and nucleic acids that carry labile charges, softens and stiffens according to the proton concentration in the surrounding environment. We also have developed an improved technique for morphological analysis of bacterial biofilms, using scanning electron microscopy, that preserves the structure of these fragile and highly hydrated materials upon drying, hence revealing finer details about biofilm architecture and cellular adhesion. Finally, we fabricatd a multichannel culture chamber from cast PDMS that allows examination of biofilms with optical instruments as well as with direct contact instruments such as an atomic force microscope.